One of the city’s most oddly successful and successfully odd bands is rolling out a new album this week.

Yes, the Born Again Floozies are back with their third release, Street Music (13 Rebellions and a Song of Consolation), which, like its predecessors, was recorded and engineered by Chicago-based studio guru Steve Albini.

What began four years ago as a lark — a husband-and-wife guitar and tap dance duo — has grown into a five-piece band with a semi-charmed life. Though it’s not a full-time pursuit for its members, the group’s sound and concept continue to generate indie media attention and invitations to play around the country.

Paste magazine, which championed the Floozies from the start, has again chosen a song for one of its monthly samplers. The new album’s opening cut, “We Got the Power (Love Letter from America),” will accompany the magazine’s October issue. The song also has been featured as a stream or download on the homepages of CMJ and Insound, the alt-rock equivalents of Rolling Stone and Amazon, and last week CMJ listed it as the No. 13 top add at college-type radio stations.

Much new material will be played live for the first time when the Floozies perform Friday at Radio Radio.

Leading the group is local music veteran Joey Welch, who writes the quirky tunes and satirical lyrics, croons like Jeff Buckley and plays rhythmic melodies on guitar with a strange two-handed tapping technique. Rounding out the current lineup are Charlie Krone on trombone, Melissa Williams on tuba, Amy Gilmore Andrus on tap dance and percussion, and Nancy Moore on percussion and backing vocals. Joining them for Friday’s show will be friends who contributed to the album, including original tap dancer Libby Milliken and guest vocalist Erika Thomas from the band Little Voice.

That instrumentation, along with bass drums, cymbals and lots of hand percussion, gives the album a surprisingly wide range of rhythms and textures, much like a passing parade. For additional ambience, friends and passersby were brought into the studio to clap and stomp.

“Like all our records, we wanted to make it as live as possible,” Welch says. “The vibe is ‘We’re on the street.’ It kind of careens out of control at times.”

Indeed, from moment to moment, the music hints at a ridiculous range of sound: rock, pop, mountain clogging, marching band, street funeral, industrial dance, you name it. Despite being anchored by tuba rather than electric bass, the  Floozies often manage to get funky, especially on the title track. When Moore and Thomas kick in on the vocals, the effect is powerful, soulful and passionate.

“There’s a definite funk influence to this, which is really unlikely,” Welch admits.

Another standout track is the Indianapolis-centric “Fly Your Flag (The Prince of 38th Street),” dedicated to the familiar street character who dances to his jam box at the intersection of 38th and College.

“I’ve been driving by that guy for years and years, and I just admired his vibe,” says Welch, who has an interview with the gentleman posted on the band’s Web site. “My hunch was that this guy was the rare kind of person who can find what makes him happy without worrying about what society says you need to be happy.”

Meanwhile, amid day jobs, family life and other concerns, the Floozies are staying as busy as they want to be. They played to thousands at a July festival in Vermont and headed out last weekend to another in Pennsylvania. They’re already booking for next summer.

“We’re doing it because it’s fun, so we can pick and choose,” Welch says. “We’re not desperate to reach some lofty illusion or goal. In our minds, this is it.”